Periodic striped ground states in Ising models with competing interactions

Abstract

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let $J$ be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent $p$ of the long range interaction is larger than $d+1$, with $d$ the space dimension, this happens for all values of $J$ smaller than a critical value $J_c(p)$, beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for $p>2d$ and $J$ in a left neighborhood of $J_c(p)$. In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes ($d=2$) or slabs ($d=3$), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.

30 pages, 7 figures, v2: references added and acknowledgments updated

References in corpus (6)

• Crystalline ground states for classical particles
• Face-centered cubic crystallization of atomistic configurations
• Phase diagram of an Ising model for ultrathin magnetic films
• Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions
• Stripe width and non-local domain walls in the two-dimensional Dipolar Frustrated Ising Ferromagnet
• Non-equilibrium structures and slow dynamics in a two dimensional spin system with competitive long range and short range interactions

Cited by in corpus (11)

• Universality of Pattern Formation
• Exact periodic stripes for a minimizers of a local/non-local interaction functional in general dimension
• Theory of partial quantum disorder in the stuffed honeycomb Heisenberg antiferromagnet
• Emergent quasicrystals in strongly correlated systems
• Pattern formation for a local/nonlocal interaction functional arising in colloidal systems
• The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations
• On the Ternary Ohta-Kawasaki Free Energy and Its One-dimensional Global Minimizers
• Asymptotically exact formulas for the stripe domains period in ultrathin ferromagnetic films with out-of-plane anisotropy
• A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains
• Big Data Information Reconstruction on an Infinite Tree for a $4\times 4$-state Asymmetric Model with Community Effects
• Variational analysis of the $J_1$-$J_2$-$J_3$ model: a non-linear lattice version of the Aviles-Giga functional